A bicycle odometer (which measures distance traveled) is attached near the.g kqm+wlp)k/ wheel hub and is designed for 27-inch wheels. What happens if you use it on a bicycle with 2p.w+q )mkklg/ 4-inch wheels?

Suppose a disk rotates at constant angular velocm nrup ib79wam+q z1ue6j8;ri d+.;y nity. Does a point on the rim have radial and/or tangential acceleration? If the disk’s angular velocity increases uniformly, does the point have radial and/or tangential ac m .ir1n pq6;nz+ e9ydbu7w ji;8+mrauceleration? For which cases would the magnitude of either component of linear acceleration change?

Could a nonrigid body be described by a single value 2o yzxjvdh pb m:gu.m9u-8))jof the angular velocity $\omega$ Explain.

Can a small force ever exert a greater t wfqz5i)asg7/orque than a larger force? Explain.

If a force $\vec{F}$ acts on an object such that its lever arm is zero, does it have any effect on the object’s motion? Explain.

Why is it more difficult to do a sit-up with your hands behindg8 985jjk kz bqugpk.; your head than when your arms are stretched out in front of you? A diagram may help you tu kj;g. 8p9jkg8 qzb5ko answer this.

A 21-speed bicycle has seven sprockets at th3x96szdpk 9tjo t9z266yfui ke rear wheel and three at the pedal cranks. In whic3djtxk oik9st2f66z 6y9 zpu9 h gear is it harder to pedal, a small rear sprocket or a large rear sprocket? Why? In which gear is it harder to pedal, a small front sprocket or a large front sprocket? Why?

Mammals that depend on being able to run fast have slender lowerycn)ajbg m7mg09t (2r legs with flesh and muscle concentrated high, close to the body (Fig. 8–34). On the basis of rotatio(gt cn 207mmj) yra9bgnal dynamics, explain why this distribution of mass is advantageous.

Why do tightrope walkers (Fig. 8–35) carrym,p jix-5b(wk a long, narrow beam?

If the net force on a system is zero, is the net torqupui uj a(88d 1k+lqj;ce also zero? If the net torque on a systq81;+caj 8 ilupdjuk(em is zero, is the net force zero?

Two inclines have the same height but makaf )qolzx*v71e different angles with the horizontal. The same steel ball is rolled down each incline. On which incline will the speed of the ball ax)7*vfo z1 alqt the bottom be greater? Explain.

Two solid spheres simultaneously star oda*h+(oiqw(e yr15qt rolling (from rest) down an incline. One sphere has twice the radius and twice the mass of the other. Which reaches the bottom of the incline first? Which has the (aiy d (hw5r oqoe*+q1greater speed there? Which has the greater total kinetic energy at the bottom?

A sphere and a cylinder h;ep eb0;z1 yd5hhxzg 9h 0td ss23r3ppave the same radius and the same mass. They start from rest at the top of an dzp; 9s g hr35zbh1epy2p ;dx03 hets0incline. Which reaches the bottom first? Which has the greater speed at the bottom? Which has the greater total kinetic energy at the bottom? Which has the greater rotational KE?

We claim that momentum and angular momentum are conserved. Yet most moving orazp/ ,xt1w yb4 rotating objects eventually 1a/y4,pwxzt bslow down and stop. Explain.

If there were a great migration of people toward the Earth’s equator, how wow lw (ia+nyk:dvkf6 *f:bi;(euld this affect the length of the daya n* f yd(6e:l+(i;wvfw:bkki?

Can the diver of Fig. 8–29 do a somersault without having any initial rot5w io-z41fc o o9ukuj t79oy9nation when she leaves the w o9fto9o4yuzj5c -o1k9i7 nu board?

The moment of inertia xgy z(we njh2.+8ky mgd7(vd*v p1z0mof a rotating solid disk about an axis through its center of masw(mn d .hekvp8mz0+ *g y (2zv17jdxygs is $\frac{1}{2}WR^2$ (Fig. 8–21c). Suppose instead that the axis of rotation passes through a point on the edge of the disk. Will the moment of inertia be the same, larger, or smaller?

Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstre an lds2e:;:nrz;wyw;tched hand. If you suddenly drop the masses, will your angular veloci2aw rey :w;;sln;dnz:ty increase, decrease, or stay the same? Explain.

Two spheres look identical and have the same massve r+ g(3hkuna85gog l(n( u-o. However, one is hollow and the other v( o8gu h 5+n3(gkler-aonu g(is solid. Describe an experiment to determine which is which.

The angular velocity of a wheel rotating oed5zii9 bc, wwdt*(3 (v8ro u4 nc9u:yrxny/ an a horizontal axle points west. In what direction is t( wtar9dyv: ue9,do (cu8in4b 3r/w c*yni 5xzhe linear velocity of a point on the top of the wheel? If the angular acceleration points east, describe the tangential linear acceleration of this point at the top of the wheel. Is the angular speed increasing or decreasing?

Suppose you are standing on the edge of a large freely rotatibs903a* c.b+sdhnq9h m.q vkfng turntable. What happens if you walk toward the ckh.+9f q*ba3sms .9vnbh0dq center?

A shortstop may leap into the air to catdv6mby+5pp rg.a ((2)d hjnahch a ball and throw it quickly. As he throws the ball, the upper part of his body rotates. If you look quickly you will noti+(pd5j a .rv )nhb6mpay2(g hdce that his hips and legs rotate in the opposite direction (Fig. 8–36). Explain.

On the basis of the law olht/lnd 3e,wn;/a8g xf conservation of angular momentum, discuss why a helicopter must have more than ond8 /hn;tew/ l3nx,alge rotor (or propeller). Discuss one or more ways the second propeller can operate to keep the helicopter stable.

  Express the following angles in radu ; *b+k)q 6fjbyqw(*kogmj: jei2(waians: (a) 30 $^{\circ} $, (b) 57 $^{\circ} $, (c) 90 $^{\circ} $, (d) 360 $^{\circ} $, and (e) 420 $^{\circ} $. Give as numerical values and as fractions of $\pi$.(Round to two decimal places)
(a)   $rad$ (b)   $rad$ (c)    $rad$ (d)    $rad$ (e)    $rad$

  Eclipses happen on Earth because of an amazing coincidence. Cj87gxs21*n avyo: vfd alculate, using the information inside the Front Cover, the angular diameters (in ray 27jovn1*8xd g vfsa:dians) of the Sun and the Moon, as seen on Earth.
Sun =    $rad$ Moon =    $rad$

  A laser beam is directed at the Moon, 380,000v9t5 smp1 7 sqrh7ky w3fk)hb4 km from Earth. The beam diverges at 377f1yvwb kp tr459h sqm)hk san angle $\theta$ (Fig. 8–37) of $1.4\times10^{-5}$ rad What diameter spot will it make on the Moon?    m

  The blades in a blender rotate at a rate of 6500 rpm. W y:sq m/lv7w;0z7qbbthen the motor is turned of7;qb0qzl 7wv m/: btsyf during operation, the blades slow to rest in 3.0 s. What is the angular acceleration as the blades slow down?    $rad/s^2$

  A child rolls a ball on a level floor 3.5 m to anx9ii 9oye (f7h 8p3usiother child. If the ball makes 15.0 revolutions, what e97hx u(i f8 oi3ps9iyis its diameter?    m

  A bicycle with tires 68 cm in diameter travels 8.0 km. How many revolutmgbs/p+0y z f3 v5kml)ions do the whk ys)vb +z0m/fg5 m3lpeels make?    $rev$

  (a) A grinding wheel 0.35 m in diameter rotates at 2500vz8da :)aa8up44. t *qedatrx rpm. Calculate its angular q4u x dd*va)8ta8 t:apr a4e.zvelocity in $rad/s$ $\omega$ =    $rad/sec$
(b) What are the linear speed and acceleration of a point on the edge of the grinding wheel? v =    $m/s$ $a_R$ =    $ m/s^2$

  A rotating merry-go-round makes one complete revolut x;ahiq 2d6313s+pxzrwe kwv *ion in 4.0 s (Fig. 8–38). (a) What is the lineap6;d s2xx erqz*3wk+iv1 3hwar speed of a child seated 1.2 m from the center?    $m/s$
(b) What is her acceleration (give components)?    $m/s^2$  ----待选择----towardsaways  the center

  Calculate the angular velocity of the Earth (a) in its orbit arv;wak )ak dnvm3qzl yv l-)a wo/eyg/3hx8809 ound the Sun    $ \times10^{-7 }$ $rad/s$
(b) about its axis.    $ \times10^{-5}$ $rad/s$

  What is the linear speedo0qqefh 3 gsp041o z:k of a point
(a) on the equator,    $m/s$
(b) on the Arctic Circle (latitude 66.5$^{\circ} $ N),    $m/s$
(c) at a latitude of 45.0$^{\circ} $ N, due to the Earth’s rotation?    $m/s$

  How fast (in rpm) must a cent j hy8re-o;mfrze* cx4) -p2dgrifuge rotate if a particle 7.0 cm from the axis of rotation is to experience an acceleration rg xhe;24rze*cfmdo8 )p-j-yof 100,000 $g’s$?    $rpm$

  A 70-cm-diameter wheel accwdltvh, + k;1nelerates uniformly about its center from 130 rpm to 280 rpm in 4.0 s. Deterh1,+lnd tvwk;mine
(a) its angular acceleration,$\approx$    $rad/s^2$(Round to one decimal places)
(b) the radial and tangential components of the linear acceleration of a point on the edge of the wheel 2.0 s after it has started accelerating. $a_R$    $m/s^2$ $a_{tan}$    $m/s^2$

A turntable of radiumpwevk1 /+m n,s $R_1$ is turned by a circular rubber roller of radius $R_2$ in contact with it at their outer edges. What is the ratio of their angular velocities, $\omega_1$ / $\omega_2$

  In traveling to the Moon, astronauts aboard the Apollo space+ np 6gm4o/ckicraft put themselves into a slow rotation to distribute the Sun’s energy evenly. At the start of their trip, they accelerated from no rotation to 1.0 revolution every minuc/4 oi+k mn6gpte during a 12-min time interval. The spacecraft can be thought of as a cylinder with a diameter of 8.5 m. Determine
(a) the angular acceleration, $\approx$    $rad/s^2$
(b) the radial and tangential components of the linear acceleration of a point on the skin of the ship 5.0 min after it started this acceleration. $a_{tan}$ =    $ \times10^{ -4}$ $m/s^2$ $a_{rad}$ =    $ \times10^{ -3}$ $m/s^2$

  A centrifuge accelerates uniformb8-swke/gr1bpa4 kc5 ly from rest to 15,000 rpm in 220 s. Through how many revolutions did it turn in t wsar5 e -kp14ckb8g/bhis time?    $rev$

  An automobile engine slows down from 4500 rpm to 1200 rpm in 2.5 s. Calcul ,jdk/cjxse . 1om3o bsa;au)*:j 9uj/pu9lsjate
(a) its angular acceleration, assumed constant,    $rad/s^2$
(b) the total number of revolutions the engine makes in this time.    $rev$

  Pilots can be tested for the stresses of flying bic: ztzbr;7uec8 l1)highspeed jets in a whirling “human centrifuge,” which takes 1.0 min 7c i;81)cl uz :ezbtrbto turn through 20 complete revolutions before reaching its final speed.
(a) What was its angular acceleration (assumed constant),    $rev/min^2$
(b) what was its final angular speed in rpm?    $rpm$

  A wheel 33 cm in diameter accelerates uniformly from 240 rpm to .p pd*2y3ckzs+graf9nz:h2 a360 rpm in 6.5 s. How far will a point on the edge of th22p3kgna h aspc9dyz .:rf+ z*e wheel have traveled in this time?    m

  A cooling fan is turned off when it is runninqgjg 70kf k9-2vugwz2g at 850rev/min It turns 1500 revolutions before it cog0fk2 q gwv2ukz79- gjmes to a stop.
(a) What was the fan’s angular acceleration, assumed constant?    $\frac{rad}{s^2}$
(b) How long did it take the fan to come to a complete stop?    s

  The tires of a car makbzs;iu f:7n kdda*lv) ;79 qmre 65 revolutions as the car reduces its speed uniformly from 959i 7qd) vbskau;n;7zrd :fm*lkm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  The tires of a car make 65 revolutions as the car reduces its speed unp,8 2psx jpd)uiformly from 95 j sp)ud28,ppxkm/h to 45km/h The tires have a diameter of 0.80 m.
(a) What was the angular acceleration of the tires? $\approx$    $rad/s^2$
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s

  A 55-kg person riding a bike puts alpcbo/v/a:b*1 d5a:r0knrx ufl her weight on each pedal when climbing a hill. The pedals rotate /b ucra01:5 o: pdvb/fanrkx*in a circle of radius 17 cm.
(a) What is the maximum torque she exerts?    $m \cdot N$
(b) How could she exert more torque?

  A person exerts a force of 55 N on the end of a door 74 vwy gklo578i,,9 i jjucm wide. What is the magn97lji g8 ,juvyko5i ,witude of the torque if the force is exerted
(a) perpendicular to the door    $m \cdot N$
(b) at a 45 $^{\circ} $ angle to the face of the door?    $m \cdot N$

  Calculate the net torque about the axle of the wheelnyyg;niz* * ,e shown in Fig. 8–39. Assume that a frictio gn*;yzy*i en,n torque of 0.4 $m \cdot N$ opposes the motion.    $m \cdot N$  ----待选择----“counterclockwiseclockwise 

Two blocks, each of mas5, gt79kwn2sko8us .d. t wjsps m, are attached to the ends of a massless rod which pivots as shown in Fig. 8–40. Initially the rod is held in the horizontal position and then released. Calcul25osws87sd . tkjt9g k, n.upwate the magnitude and direction of the net torque on this system.

  The bolts on the cylinal0htqi5:b-z der head of an engine require tightening to a torque of 38 5 q-0bhztl: ai$m \cdot N$ If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?    N
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench (Fig. 8–41).    N

  Determine the moment of inertia of a 10.8-kg sphere of radius 0.648 m when th)o w-l 6if:uaww7(xnee axis of rotation is thri lw:(fww)o-ae u 67xnough its center.    $kg \cdot m^2$

  Calculate the moment of inert/ dld 2njh7ii4g .)sm4vm6 jplia of a bicycle wheel 66.7 cm in diameter. The rim and tire have a cgp/sih4 dn7.2l mv m d4j)i6ljombined mass of 1.25 kg. The mass of the hub can be ignored (why?).    $kg \cdot m^2$

  A small 650-gram ballwz;j x9od8pn f+(k j2o on the end of a thin, light rod is rotated in a horizontal circle ofj9w z2+(dfpk o;o8jxn radius 1.2 m. Calculate
(a) the moment of inertia of the ball about the center of the circle,    $kg \cdot m^2$
(b) the torque needed to keep the ball rotating at constant angular velocity if air resistance exerts a force of 0.020 N on the ball. Ignore the rod’s moment of inertia and air resistance.    $m \cdot N$

  A potter is shaping a bowl on 40aww h+fua eo (;rlz0)mkz (ra potter’s wheel rotating at constant angular speed (Fig. 8–42). The friction force between m ()+k fal(z r0eo;wwahrz40uher hands and the clay is 1.5 N total.
(a) How large is her torque on the wheel, if the diameter of the bowl is 12 cm?    $m \cdot N$
(b) How long would it take for the potter’s wheel to stop if the only torque acting on it is due to the potter’s hand? The initial angular velocity of the wheel is 1.6 rev/s, and the moment of inertia of the wheel and the bowl is 0.11 $kg \cdot m^2$.    s

  Calculate the moment of inertia of the array of pjay6bd:b; /51ifv5 wqlw)j v yoint objects shown in Fig. 8–43 )qv1wjv:bbljwia/ yy f d;556about
(a) the vertical axis,    $kg \cdot m^2$
(b) the horizontal axis. Assume m=1.8 kg,M=3.1kg and the objects are wired together by very light, rigid pieces of wire. The array is rectangular and is split through the middle by the horizontal axis.    $kg \cdot m^2$
(c) About which axis would it be harder to accelerate this array?

  An oxygen molecule consists of two oxygen ato6d 3frv-l5gd/ yid9n kms whose total mass is $5.3 \times10^{ -26}$ kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is $ 1.9\times10^{-46 }$ $kg \cdot m^2$ From these data, estimate the effective distance between the atoms.    $\times10^{-10 }$ m

  To get a flat, uniform r.)g/me7 lz rkcylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. 8–44. If the satellite has a mass of 3600 kg and a radius of 4.0 m, what is the required steady force of each rocket if the satellite is to rer z)/egkr7 lm.ach 32 rpm in 5.0 min? $\approx$    N(round to the nearest integer)

  A grinding wheel is a uniform cylinder with a radius of 85rk g--ij 1c.ipfsi;y.50 cm and a mass of 0.580 kg. Calcula1;j -.gsf ki y-5ipricte
(a) its moment of inertia about its center, $\approx$    $kg \cdot m^2$
(b) the applied torque needed to accelerate it from rest to 1500 rpm in 5.00 s if it is known to slow down from 1500 rpm to rest in 55.0 s。    $m \cdot N$

  A softball player swz(j; f*/aeif g j)bh1lings a bat, accelerating it from rest to 3 $rev/s$ in a time of 0.20 s. Approximate the bat as a 2.2-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.    $m \cdot N$

  A teenager pushes tangentially on a small hand-driven merc2 /gpgyrt9+ -:wt(s)vwy)ap xj 5wz wry-go-round and is able to accelerate it from rest to a frequency of 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 760 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque rew)r g+a:p 5vgwsyc p9j2)z/ y(wx- twtquired to produce the acceleration, neglecting frictional torque. $\approx$   $m \cdot N$ What force is required at the edge?    N

  A centrifuge rotor rotating at 10,300)f97w twu 7tgu5zda v6e/r(ng rpm is shut off and is eventually brought uniformly to rest by a frictionalnwdtu 9z6 g)g75w(/ 7treav uf torque of 1.2 $m \cdot N$ If the mass of the rotor is 4.80 kg and it can be approximated as a solid cylinder of radius 0.0710 m, through how many revolutions will the rotor turn before coming to rest,    $rev$ how long will it take?    s

  The forearm in Fig. 8–45 accvze +s6* .5v mu2jiccrelerates a 3.6-kg ball at 7 $m/s^2$ by means of the triceps muscle, as shown. Calculate
(a) the torque needed,    $m \cdot N$
(b) the force that must be exerted by the triceps muscle. Ignore the mass of the arm.    N

  Assume that a 1.00-kg ball is thrown solcjv/:; mc q(rvely by the action of the forearm, which rotates about the elbow joint under the action of the triceps muscle, Fig. 8–45. The ball is acceleratedqr;v:m vcj (c/ uniformly from rest to 10 $m/s$ in 0.350 s, at which point it is released. Calculate
(a) the angular acceleration of the arm,    $rad/s^2$
(b) the force required of the triceps muscle. Assume that the forearm has a mass of 3.70 kg and rotates like a uniform rod about an axis at its end.    N

  A helicopter rotor blade can be considered a long thin rod, as showsyxsd:9 ijnb-7xvi8: n in Fig. 8–46.i b-d:xjvsy:7is n9 x8
(a) If each of the three rotor helicopter blades is 3.75 m long and has a mass of 160 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation.    $kg \cdot m^2$
(b) How much torque must the motor apply to bring the blades up to a speed of 5 $rev/s$ in 8.0 s?    $m \cdot N$

An Atwood’s machine consists of two masses,dky1x/03h2w5kxm7 +pz;5 svtrhhl tqxomt5 . $m_1$ and $m_2$ which are connected by a massless inelastic cord that passes over a pulley, Fig. 8–47. If the pulley has radius R and moment of inertia I about its axle, determine the acceleration of the masses $m_1$ and $m_2$ and compare to the situation in which the moment of inertia of the pulley is ignored. [Hint: The tensions $F_{T1}$ and $F_{T2}$ are not equal. We discussed this situation in Example 4–13, assuming for the pulley.]

  A hammer thrower accelerates the hammer from rest within four full turns (revrvw2tdx4.b m 8v/72o ug sa4wzeik+5wolutions5itmwbw2oruawz /.2d x vg4v78ek4 s+) and releases it at a speed of 28 $m/s$ Assuming a uniform rate of increase in angular velocity and a horizontal circular path of radius 1.20 m, calculate
(a) the angular acceleration,    $rad/s^2$
(b) the (linear) tangential acceleration,    $m/s^2$
(c) the centripetal acceleration just before release,    $m/s^2$
(d) the net force being exerted on the hammer by the athlete just before release,    N
(e) the angle of this force with respect to the radius of the circular motion.    $^{\circ} $

  A centrifuge rotor has a moment of inertia d2 )e0yyl*3n fu4nkrp of $3.75 \times10^{-2 }$ $kg \cdot m^2$ How much energy is required to bring it from rest to 8250 rpm?    J

  An automobile engine develo7+pyzjl ;i1zxps a torque of 280 $m \cdot N$ at 3800 rpm. What is the power in watts and in horsepower?    W    hp

  A bowling ball of mass 7.3 kg and radixyo/ilqjoj.*qae)-r1k x y vj cc7;j h-+f0,ius 9.0 cm rolls without slipping down a lane a) c+x-ox.i-jhkje 1cv;j0qo i*ylra j/yqf,7t 3.3 $m/s$ Calculate its total kinetic energy.    J

  Estimate the kinetic energy of the Earth with respect to the Sun as the sum of tl-yi9ixx: q, ;ln*b ujg+am4 sis2v*d w xi*2;qdv,bnj+s-l:sim uxgia*4l9 yo terms,
(a) that due to its daily rotation about its axis,$KE_{daily}$=    $\times10^{29 }$ J
(b) that due to its yearly revolution about the Sun. $KE_{yearly}$+    $\times10^{33 }$ J [Assume the Earth is a uniform sphere with $6 \times10^{ 24}$ kg and $6.4 \times10^{6 }$ m and is $1.5 \times10^{8 }$ km from the Sun.]$KE_{daily}$ + $KE_{yearly}$ =    $ \times10^{33 }$ J

  A merry-go-round has a mass of 1640 kg and a radius of 7.5yi- ydz24 y9xz0 m. How much net work is required dizxy9 yy4-z2to accelerate it from rest to a rotation rate of 1.00 revolution per 8.00 s? Assume it is a solid cylinder.    J

  A sphere of radius 2g1j/ujf7 jrr2 ek;jh70.0 cm and mass 1.80 kg starts from rest and rolls without slipping down a 30hj r;1kjg2j eur7j /7f.0 $^{\circ} $ incline that is 10.0 m long.
(a) Calculate its translational and rotational speeds when it reaches the bottom. $v_{CM}$ =    $\omega$ =    $rad/s$
(b) What is the ratio of translational to rotational KE at the bottom?    Avoid putting in numbers until the end so you can answer:
(c) do your answers in (a) and (b) depend on the radius of the sphere or its mass?

  Two masses, $m_1$ = 18 kg and $m_2$ = 26.5 kg are connected by a rope that hangs over a pulley (as in Fig. 8–47). The pulley is a uniform cylinder of radius 0.260 m and mass 7.50 kg. Initially, is on the ground and $m_2$ rests 3.00 m above the ground. If the system is now released, use conservation of energy to determine the speed of $m_2$ just before it strikes the ground. Assume the pulley is frictionless.    $m/s$

  A 2.30-m-long pole is balanced vertically on itys;(9 uqm0 sek) znpe p+8l+sps tip. It starts to fall and its lower end does not slip. What mpy++sz(q 0p lesu;s)npe8 k9 will be the speed of the upper end of the pole just before it hits the ground? [Hint: Use conservation of energy.]    $m/s$

  What is the angular momed0 9hzbf- *gaigjnz*4ntum of a 0.210-kg ball rotating on the end of a thin string ig9g-zzb*dj nh i0fa4*n a circle of radius 1.10 m at an angular speed of 10.4 $rad/s$?    $kg \cdot m^2$

  (a) What is the angular mr32(ajwcl8 t4*fb;t g 2mlh5kgcd 9 szomentum of a 2.8-kg uniform cylindrical grinding wheel o8t3m5cl kl2rs a9;4b*w gctjz h dgf2(f radius 18 cm when rotating at 1500 rpm?    $kg \cdot m^2$
(b) How much torque is required to stop it in 6.0 s?    $m \cdot N$

A person stands, hands at his side, on a platform that is rotating at +sv -o*hld2hv a rate of 1.3rev/s If he raises his arms to a horizontal positiol+h-v2* sdo vhn, Fig. 8–48, the speed of rotation decreases to 0.8 $rev/s$ (a) Why?
(b) By what factor has his moment of inertia changed?

  A diver (such as the one shown in Fig. 8–29)ode4x d4c,*1h j) 2cwvbr3qcr can reduce her moment of inertia by a factor of about 3.5 when changing from the straight posiqc c ) x*jcr4wvbh ,d32o41rdetion to the tuck position. If she makes 2.0 rotations in 1.5 s when in the tuck position, what is her angular speed ($rev/s$) when in the straight position?   $rev/s$

  A figure skater can increase her spin rot3xcq cv** vj x8ts9ce,ation rate from an initial rate of 1.0 rev every 2.cs89*c , qv3j*t xvxec0 s to a final rate of 3 $rev/s$ If her initial moment of inertia was 4.6 kg*$m^2$ what is her final moment of inertia? How does she physically accomplish this change?    $kg \cdot m^2$

  A potter’s wheel is rot er 48/ 1bqfke2ktfa6oating around a vertical axis through its center at a frequency of 1.5rev/s The wheel can be considered a uniform disk of mass 5.0 kg and diameter 0.40 m. The potter then throws a 3.1-kg chunk of clay, fq2ar /bk41o6tek8ef approximately shaped as a flat disk of radius 8.0 cm, onto the center of the rotating wheel. What is the frequency of the wheel after the clay sticks to it?    $rev/s$

  (a) What is the angulat(xd8u (;ziph r momentum of a figure skater spinning at 3.5 $rev/s$ with arms in close to her body, assuming her to be a uniform cylinder with a height of 1.5 m, a radius of 15 cm, and a mass of 55 kg?    $kg \cdot m^2$
(b) How much torque is required to slow her to a stop in 5.0 s, assuming she does not move her arms?    $m \cdot N$

  Determine the angular momentum of the b r3pt:e6(hbv sd.j-sEarth
(a) about its rotation axis (assume the Earth is a uniform sphere),    $\times 10^{33} \; kg \cdot m^2$
(b) in its orbit around the Sun (treat the Earth as a particle orbiting the Sun). The Earth has mass $6 \times 10^{24} \; kg$ and radius $6.4 \times 10^{6} \; m$ and is $1.5 \times 10^{8} \; km$ from the Sun.    $\times10^{40} \; kg \cdot m^2$

A nonrotating cylindrical disk of moment of inertia I is drop;.twmwh- *ts*l /atopped onto an identical disk rotatingo/wttl ; msaw p*th.*- at angular speed $\omega$ Assuming no external torques, what is the final common angular speed of the two disks?

  A uniform disk turns at 2.4 5/n 8a4o zpvav+h gpa3$rev/s$ around a frictionless spindle. A nonrotating rod, of the same mass as the disk and length equal to the disk’s diameter, is dropped onto the freely spinning disk, Fig. 8–49. They then both turn around the spindle with their centers superposed. What is the angular frequency in rev/s of the combination?    $rev/s$

  A person of mass 75 kg stands at the centefgq0*op of vi8 gz6;:dr of a rotating merry-go-round platform of radz:8*ggf d pfqi0 v;oo6ius 3.0 m and moment of inertia 920 $kg \cdot m^2$ The platform rotates without friction with angular velocity 2 $rad/s$ The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.    $rad/s$
(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person’s walk.$KE_i$ =    J $KE_f$ =    J

  A 4.2-m-diameter merry-go-round is rotating freely with an angula.+yx,vqwzdd0f sy94o: ro a r8 ahf43pr velocity of 0.w9 zd y,rh.0 a3:+vs48 qadyfpofro4x 8 $rad/s$ Its total moment of inertia is 1760 $kg \cdot m^2$ Four people standing on the ground, each of mass 65 kg, suddenly step onto the edge of the merry-go-round. What is the angular velocity of the merry-go-round now?    $rad/s$ What if the people were on it initially and then jumped off in a radial direction (relative to the merry-go-round)?    $rad/s$

  Suppose our Sun eventually collapsejp /znq pl6qi0, -h7w w1wsr)is into a white dwarf, losing about half its mass in the process, and winding up with a radius 1.0% of its existing radius. Assuming the lost mass carries away no angular momentum, what would tlw/67i01ws,-) pqzpnr wi jhqhe Sun’s new rotation rate be?(round to the nearest integer)$\approx$    $rad/s$ (Take the Sun’s current period to be about 30 days.) What would be its final KE in terms of its initial KE of today?$KE_{f}$=    $KE_{i}$

  Hurricanes can involve winds in excess of 5z3v 3g1cjd ckas ;w*w120 $km/h$ at the outer edge. Make a crude estimate of
(a) the energy,    $ \times10^{16 }$ J
(b) the angular momentum, of such a hurricane, approximating it as a rigidly rotating uniform cylinder of air (density 1.3 $kg \cdot m^2$) of radius 100 km and height 4.0 km.    $ \times10^{20 }$ $kg \cdot m^2$

  An asteroid of mass 5ue;i5w2uwnc jge9x+$ 1.0\times10^{ 5}$ traveling at a speed of relative to the Earth, hits the Earth at the equator tangentially, and in the direction of Earth’s rotation. Use angular momentum to estimate the percent change in the angular speed of the Earth as a result of the collision.    $\times10^{-16 }$ %

A person stands on a plaz3bf;* 7 z d2luxj5grkz u4zkx6ea3t.tform, initially at rest, that can rotate freely without friction. The moment of inertia of the perz 5k 3rf34zdlj gx6t*bu2kzae uz; .7xson plus the platform is $I_P$ The person holds a spinning bicycle wheel with its axis horizontal. The wheel has moment of inertia $I_W$ and angular velocity $\omega_W$ What will be the angular velocity $\omega_W$ of the platform if the person moves the axis of the wheel so that it points (a) vertically upward, (b) at a 60º angle to the vertical, (c) vertically downward? (d) What will $\omega_P$ be if the person reaches up and stops the wheel in part (a)?

  Suppose a 55-kg person stands at the edge of a 6.5-m dih+5sqfb9i2v /o gqtti.w .k, eameter merry-go-round turntable that is i5 sobg, hqi 9t/fk+v.t2ew. qmounted on frictionless bearings and has a moment of inertia of 1700 $kg \cdot m^2$ The turntable is at rest initially, but when the person begins running at a speed of 3.8 $m/s$ (with respect to the turntable) around its edge, the turntable begins to rotate in the opposite direction. Calculate the angular velocity of the turntable.    $rad/s$

A large spool of rope rolls onu,o bhkvy49et : 4;ta+jd qyp4 the ground with the end of the rope lying on the top edge of the spool. A person grabs the end of the rope and walks a distance L, holding onto it, Fig. 8–50. The spool rolls behind the person wi49th4qk ytp+ jby:douv 4;, eathout slipping. What length of rope unwinds from the spool? How far does the spool’s center of mass move?

  The Moon orbits the Earth such that the same side always faces thecb9 s /dt2kcd00tbx/b Earth. Determine the ratio of the Moon’s spin angular momentum (about its own axis) to its ob0t tbcdb2 /d9/c0s xkrbital angular momentum. (In the latter case, treat the Moon as a particle orbiting the Earth.)    $\times10^{ -6}$

  A cyclist accelerates from rest at a rate of 1 x erds:q6rdg)3 oi.3l m/$s^2$ How fast will a point on the rim of the tire at the top be moving after 3.0 s? [Hint: At any moment, the lowest point on the tire is in contact with the ground and is at rest — see Fig. 8–51.]    $m/s$

  A 1.4-kg grindstone in the shape of a uniform cylinder of radius 0.20 m acqei fkgsm-*:-n uires a rotational rate of from rest over a 6.0-s interval at constant angular acceleration. Calculate the ton-:-sfg ek m*irque delivered by the motor.    $m \cdot N$

  (a) A yo-yo is made of two solid cylindrical disks, each of mass 0.050 kg and op h dfxx2 2vm/a8ae*g (w6ax:diameter 0.075 m, joined by a (concentric) thin solid cylindrical hub of mas/whx(26 8x v:dxp2ama*afg eos 0.0050 kg and diameter 0.010 m. Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0-m-long string, if it is released from rest.    $m/s$
(b) What fraction of its kinetic energy is rotational?    %

  (a) For a bicycle, how is the angular speed of the rear wpt*aix2onq/+0bck e+* z z 8owheel ($\omega_R$) related to that of the pedals and front sprocket ($\omega_F$) Fig. 8–52? That is, derive a formula for ($\omega_R$)/($\omega_F$) Let $N_F$ and $N_R$ be the number of teeth on the front and rear sprockets, respectively. The teeth are spaced equally on all sprockets so that the chain meshes properly.
(b) Evaluate the ratio ($\omega_R$)/($\omega_F$) when the front and rear sprockets have 52 and 13 teeth, respectively,   
(c) when they have 42 and 28 teeth.   

  Suppose a star the si 8kc: -w2:,vxjx xss xih7lmx(ze of our Sun, but with mass 8.0 times as great, were rotating at a speed of 1.0 revolution every 12 days. If it were to undergo gravitational vh:2c7jwx 8-smisxxxx( k: ,l collapse to a neutron star of radius 11 km, losing three-quarters of its mass in the process, what would its rotation speed be? Assume that the star is a uniform sphere at all times, and that the lost mass carries off no angular momentum.    $\times10^{9 }$ $rev/day$

  One possibility for a low-pollution automobile is for it to use energy st; aag7uty; u,n4b rz3xored in a heavy rotating flywheel. Suppose such a car has a total mass of 1400 kg, uses a uniform ;3urtaung ; bzxay7,4cylindrical flywheel of diameter 1.50 m and mass 240 kg, and should be able to travel 350 km without needing a flywheel “spinup.”
(a) Make reasonable assumptions (average frictional retarding force = 450N twenty acceleration periods from rest to equal uphill and downhill, and that energy can be put back into the flywheel as the car goes downhill), and show that the total energy needed to be stored in the flywheel is about $ 1.7\times10^{8 }$J.    $ \times10^{ 8}$ J
(b) What is the angular velocity of the flywheel when it has a full “energy charge”?    $rad/s$
(c) About how long would it take a 150-hp motor to give the flywheel a full energy charge before a trip? $\approx$    min

  Figure 8–53 illustrates anhbi6x) -80 icj d-ggpa $H_2O$ molecule. The O–H bond length is 0.96 nm and the H–O–H bonds make an angle of 104 $^{\circ} $. Calculate the moment of inertia for the $H_2O$ molecule about an axis passing through the center of the oxygen atom
(a) perpendicular to the plane of the molecule,    $\times10^{-45 }$ $kg \cdot m^2$
(b) in the plane of the molecule, bisecting the H–O–H bonds.    $ \times10^{-45 }$ $kg \cdot m^2$

  A hollow cylinder (hoop) is rolling on a horizontal surface at speed v=3.3 )ig 9wokwgd5 xcpdx kf45*7l 7$m/s$ when it reaches a 15 $^{\circ} $ incline.
(a) How far up the incline will it go? $\approx$    m (round to one decimal place)
(b) How long will it be on the incline before it arrives back at the bottom?    s

A uniform rod of mass M and length L can pivot freely (i.e., we is pb*usufa o:0f4s2xo (cu8b(gnore friction) about a hinge attached to a wall, as in Fig. 8–54. The rod is held horizontally and then released. At the moment of release, determine (a) the angular acceleration of the rod, and (b) the linear acceleration of the tip of the rod. Assume that the force of grav8bfub: (oc02o u(x4p*fsssua ity acts at the center of mass of the rod, as shown. [Hint: See Fig. 8–21g.]

A wheel of mass M has radius R. It is standing vertically on the floor 34zpp+gcdb*1o2 5nl zptay)s , and we want to exert a horizontal force F at its axle so that it will climb a step against which it rests (Fig. 8–55). The step d)nz2*3lpt1 ppbg+c 4asoyz5 has height h, where h

  A bicyclist traveling with speed v=4.2m/s on a flat rj9t,k,lza9o t oad is making a turn with a radius The forces acting on the cl9ta o ,9,ztkjyclist and cycle are the normal force $\left(\mathbf{\vec{F}}_{\mathrm{N}}\right)$ and friction force $\left(\mathbf{\vec{F}}_{\mathbf{fr}}\right)$ exerted by the road on the tires, and $m\vec{\mathbf{g}}$ the total weight of the cyclist and cycle (see Fig. 8–56).
(a) Explain carefully why the angle $\theta$ the bicycle makes with the vertical (Fig. 8–56) must be given by tan $\tan\theta=F_{\mathrm{fr}}/F_{\mathrm{N}}$ if the cyclist is to maintain balance.(round to the nearest integer)
(b) Calculate $\theta$ for the values given.    $^{\circ} $
(c) If the coefficient of static friction between tires and road is $\mu_s=0.70$ what is the minimum turning radius?    m

  Suppose David puts a 0.50-kg rt+xx9m cdz9c*8sxi a3cq * zn5ock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle above his head, accelerating it from rest to a rate of 120 rpm after 5.0 s. What is the torque rencxd*cs3xac 9z9 q*8 z5imtx+quired to achieve this feat, and where does the torque come from?    $m \cdot N$

  Model a figure skater’s body as a solid cylinder a y1vi0jrt0p +ynd her arms as thin rods, making reasonable estimates for the dimensions. Then calculate the ratio of the angular speeds for a spinning skater with outstretched arms, and with arms held tightly against her +0 tyy0ivpj r1body.   

  You are designing a clutch assembly whi 5p+e9l ot4nidch consists of two cylindrical plates, of ed4 o9l tpi5n+mass $M_{\mathrm{A}}=6.0$ $\mathrm{kg}$ and $M_{\mathrm{B}}=9.0$ $\mathrm{kg}$ with equal radii R=0.60 $\mathrm{m}$ They are initially separated (Fig. 8–57). Plate $M_{\mathrm{A}}$ is accelerated from rest to an angular velocity $\omega_1=7.2$ $\mathrm{rad/s}$ in time $\Delta t=2.0$ s Calculate
(a) the angular momentum of $M_{\mathrm{A}}$    $kg \cdot m^2$
(b) the torque required to have accelerated $M_{\mathrm{A}}$ from rest to $\omega_{1}$    $m \cdot N$
(c) Plate $M_{\mathrm{B}}$ initially at rest but free to rotate without friction, is allowed to fall vertically (or pushed by a spring), so it is in firm contact with plate $M_{\mathrm{A}}$ (their contact surfaces are high-friction). Before contact, $M_{\mathrm{A}}$ was rotating at constant $\omega_{1}$ After contact, at what constant angular velocity $\omega_{s}$ do the two plates rotate?    $rad/s$

  A marble of mass m and radius r rolls along the looped rough trye2u de7/*r9r rii0 wrack of Fig. 8–58. What is the minimum value of the vertical height h that the marble must drop if it is to reach the highest point of the loop without leyrr9iwe 02ud r/7ei*raving the track? Assume $r\ll R$ and ignore frictional losses. h =    R

  Repeat Problem 84, but do np67sok+ow 8 u1 esd7jkot assume $r\ll R$ h =    (R-r)

  The tires of a car make 85 revolutions as the carjbj x/ufm2 )5tl;r j-u reduces its speed uniformly from 90km/h to 60km/h The tires have 5bx-jmj2;rt f/luuj )a diameter of 0.90 m. (a) What was the angular acceleration of each tire? $\approx$    $rad/s^2$(round to two decimal place)
(b) If the car continues to decelerate at this rate, how much more time is required for it to stop?    s